Question

[Help Please!] Find the value of x.

Answer 1

x = 52 degrees

Explanation:

Let's first focus on the angle x + 72. Immediately adjacent to x + 72 is angle RQS. These two angles are "straight" in that they lie immediately adjacent to one another and add up to 180 degrees. Then angle RQS can be expressed as

180 degrees - (x + 72 degrees), or 108 - x degrees.

The three interior angles of the triangle must add up to 180 degrees. Hence

108 - x degrees + 34 degrees + 90 degrees = 180 degrees, and so:

108 - x + 34 = 90

This yields x = 52 degrees.

Answer 2

x = 52

Explanation:

The exterior angle is equal to the sum of the opposite interior angles of a triangle

x+72 = 34+90

x +72 =124

Subtract 72 from each side

x = 124-72

x =52